Advances and Applications in Statistics
Volume 24, Issue 1, Pages 35 - 48
(September 2011)
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EM ALGORITHM FOR THE MIXTURES OF THE MARSHALL-OLKIN BIVARIATE
WEIBULL DISTRIBUTIONS
Nazif Çalış, Ayça Hatice Türkan, Murat Erişoğlu, Ülkü Erişoğlu and Hamza Erol1
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Abstract: In lifetime and reliability data analysis, Exponential, Weibull and Gamma distributions are widely used to model univariate homogeneous data and mixtures of these distributions are used to model heterogeneous data. In case of two variables, Marshall-Olkin bivariate exponential distribution (MOBE) and Marshall-Olkin bivariate Weibull distribution (MOBW) can be used. In this study, mixture of MOBW distributions is considered for heterogeneous bivariate data. Unlike other finite mixture model studies, this study includes mixture of partial density functions. The maximum likelihood estimators for the mixture of MOBW distributions will be calculated by EM algorithm. We perform some simulations to see the performance of the EM algorithm and analyze football data set for illustrative purpose. |
Keywords and phrases: EM algorithm, Marshall-Olkin bivariate Weibull, maximum likelihood estimation, mixture distribution models. |
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